Three bars having lengths l, 2l,and 3l and ar | vedclass

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(C) The total extension of the compound rod is the sum of the extensions of the individual bars.Let the extensions be $x_1, x_2$,and $x_3$ for the thr

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$\frac{3Fl}{AY}$

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(C) The total extension of the compound rod is the sum of the extensions of the individual bars.Let the extensions be $x_1, x_2$,and $x_3$ for the three bars respectively.The formula for extension is $\Delta l = \frac{Fl}{AY}$.For the first bar: $x_1 = \frac{Fl}{AY}$.For the second bar: $x_2 = \frac{F(2l)}{(2A)Y} = \frac{Fl}{AY}$.For the third bar: $x_3 = \frac{F(3l)}{(3A)Y} = \frac{Fl}{AY}$.The total extension $x = x_1 + x_2 + x_3 = \frac{Fl}{AY} + \frac{Fl}{AY} + \frac{Fl}{AY} = \frac{3Fl}{AY}$.

Three bars having lengths $l, 2l$,and $3l$ and areas of cross-section $A, 2A$,and $3A$ are joined rigidly end to end. The compound rod is subjected to a stretching force $F$. The total increase in the length of the rod is (Young's modulus of the material is $Y$ and the bars are massless).

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